A fundamental invariant associated to every rational function is its monodromy group. We shall discuss the accumulating group theoretic work towards determining the complex rational functions with a specified monodromy group, and its applications to problems concerning values of rational functions over finite fields, Hilbert irreducibility, Nevanlinna theory, and Mazur's torsion theorem.
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12. May15:30  16:30
Location: 48436AG Algebra, Geometrie und ComputeralgebraDanny Neftin (University of Michigan, Ann Arbor): Monodromy groups of rational functions

21. May15:30  16:30
Location: 48438AG Algebra, Geometrie und ComputeralgebraAndreas Steepaß (TU Kaiserslautern): Semaphores
Semaphores are data structures which can be used to manage restricted
resources in concurrent programming. For example, Singular's parallel
framework uses a semaphore to ensure that the number processes running
in parallel is bounded by some userdefinable integer. In this talk, we
will first show how basic synchronisation patterns such as mutexes,
rendezvous, and barriers can be implemented by means of semaphores.
Based on these ingredients, we will then focus on more complicated
situations such as the readerswriters problem or the dining
philosophers problem. The challenge is to find elegant solutions which
do not cause deadlocks or starvation. 
21. May17:00  18:00
Location: 48519AG Algebra, Geometrie und ComputeralgebraVivien Ripoli (Universität Wien): Coxeter elements in wellgenerated complex reflection groups
Coxeter elements are specific elements in a reflection group W, that play a key role in CoxeterCatalan combinatorics, in particular in the construction of the Wnoncrossing partition lattice. Several nonequivalent definitions coexist in the literature. I will explain and motivate the following: for W an irreducible real reflection group, or a wellgenerated complex reflection group, a Coxeter element in $W$ is an element having an eigenvalue of order h (where $h$ is the highest invariant degree of $W$, also known as Coxeter number). The set of these elements does not always form a unique conjugacy class, but it forms a unique orbit under the action of reflection automorphisms of W. Using a Galois action on these elements, we obtain that the number of conjugacy classes is equal to the degree of the field of definition of $W$. When $W$ is real, $c$ is a Coxeter element if and only if there exists a simple system $S$ constituted of reflections and such that $c$ is the product of the elements in $S$. Finally I will explain how some of the properties of these Coxeter elements can be extended to Springerregular elements. (Joint work with Vic Reiner and Christian Stump)